I’ve wire-wrapped with 14k with no problems. If cost is at all a
concern for you, I recommend doing the piece in copper first, so
that you know exactly how much wire you will need and what you plan
to do with it. Then, to paraphrase the carpenters, measure five
times, cut once. And work slowly.
If, however, money is no object, you could easily use 18k. Higher
karats will depend on what you’re doing and how well you need it to
hold its shape. For the ultimate in luxury, there’s always
Puregold–24k that can be “oven-hardened” like Argentium Sterling.
Also, if money is no object, the choice can be more influenced by
aesthetics. Personally, I think 14k looks a little washed out with
certain colors, so I simply don’t combine them. If I could afford
to, I would just use a higher karat.